 Hello and welcome to the session. Let's work out the following problem. It says, draw the graphs of the equation 4x-y-8 is equal to 0, 2x-3y, plus 6 is equal to 0. Also determine the vertices of the triangle formed by the lines and the x-axis. So let's now move on to the solution. The first equation given to us is 4x-y-8 is equal to 0 and this can be written as 4x-y is equal to 8. And the second equation is 2x-3y, plus 6 is equal to 0 and this can be written as 2x-3y is equal to minus 6. Now from this we have y is equal to 4x-8 and from this we have y is equal to minus y is equal to 2x-6 upon 3. Now to draw the graph of these equations we need to make a table which gives us the points through which the graph passes through. Now we will give different values to x and obtain its corresponding value of y. So now if we put x is equal to 2, y will be 4 into 2 minus 8 that is 8 minus 8 that is 0. Now if we put y, x is equal to 1 so it will be 4 into 1 minus 8 that is minus 4. So if x is 1 y is minus 4 and if we put x is equal to 3 we have 4 into 3 minus 8 that is 12 minus 8 that is 4. So if x is 3 y is 12 minus 8 that is 4. Now we draw the graph of the equation 4x-y minus 8 is equal to 0 or 4x-y is equal to 8 and this is the corresponding table. Now if we have x is equal to 1 then y is equal to minus 4 that is this point and this point is 1 minus 4 and if x is 2 that is 0 then y is 0. Now this is the x-axis which is the line y is equal to 0 so this is the point 2-0 and if x is 3 y is 4 this is the point 3-4. Now we join these three points to get the graph of this equation. So this is the line 4x-y minus 8 is equal to 0. Now we make a table for the second equation if x is 0 then y is 6 upon 3 that is 2. So we have x is 0 y is 2 and if we have x is equal to 3 so y will be 2 into 3 plus 6 that is 6 plus 6 divided by 3 that is 12 divided by 3. So we have x is 3 12 divided by 3 is 4 and if we put x is equal to minus 3 then y will be equal to 2 into minus 3 plus 6 that is minus 6 plus 6 by 3 so this is 0. Now we draw the graph of the equation 2x-3y is equal to 6 and this is the corresponding table. Now if x is 0 y is 2 this is the point 0-2 and if x is 3 y is 4 so this is the point 3-4 and if x is minus 3 that is here then y is 0. So this is the point minus 3-0. Now we join these three points to get the graph of the equation 2x-3y is equal to 6. So this is the line 2x-3y is equal to 6 and this is the triangle formed by the two lines and the x axis this is the x axis. So let's name this triangle as A, B, C and we see that the vertices of these triangles are 3-4 minus 3-0 and 2-0. So the vertices of triangle A, B, C A has coordinates 3-4 B has coordinates minus 3-0 the coordinate of the point C is 2-0. So this is the required triangle A, B, C and the vertices are 3-4 minus 3-0 and 2-0. So this completes the question and the session by for now take care have a good day.